In a random thinning operation, each point of the pattern X
is randomly either deleted or retained (i.e. not deleted).
The result is a point pattern,
consisting of those points of X
that were retained.
Independent random thinning means that the retention/deletion of each
point is independent of other points.
The argument P
determines the probability of retaining
each point. It may be
- a single number,
so that each point will be retained with
the same probability P
;
- a vector of numbers,
so that the i
th point of X
will be retained with probability P[i]
;
- a function
P(x,y)
, so that a point at a location
(x,y)
will be retained with probability P(x,y)
;
- a pixel image,
containing values of the retention probability
for all locations in a region encompassing the point pattern.
If P
is a function, it should be ‘vectorised’, that is,
it should accept vector arguments x,y
and should yield a
numeric vector of the same length. The function may have extra
arguments which are passed through the …
argument.